Paper Citation Record · LEDGER

A primer on the closure of algebraic complexity classes under factoring

As of 7 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 1 inbound Pith citation observation for arXiv:2506.19604.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.19604 v2

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T23:14:16.671894Z

measured 39 of 39 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-26T01:44:09.049816Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-07-04T15:19:56.574104Z

Reference resolution

38 of 38 outbound references displayed

verified exact0
verified fuzzy12
unresolved26
parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 301775f5-8a05-4430-9615-1c7a619e16e1 · outbound

This paper cites Proving Lower Bounds via Pseudo-Random Gen- erators.

A primer on the closure of algebraic complexity classes under factoring Proving Lower Bounds via Pseudo-Random Gen- erators

Reference 1

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Source-reported events for the cited work

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Observation b4427145-84dc-4820-ae4a-36272faee7d6 · outbound

This paper cites Cook’s versus Valiant’s Hypothesis.

A primer on the closure of algebraic complexity classes under factoring Cook’s versus Valiant’s Hypothesis

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T23:14:11.826285Z

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Observation 73f414b6-ede9-4ce8-bbd0-7f0dfa047bc4 · outbound

This paper cites Completeness classes in algebraic complexity theory.

A primer on the closure of algebraic complexity classes under factoring Completeness classes in algebraic complexity theory

Reference 10

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Observation a9e2c5a3-5e35-40fc-8b9d-66e9130e3668 · outbound

This paper cites Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic Circuits.

A primer on the closure of algebraic complexity classes under factoring Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic Circuits

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T23:14:12.870541Z

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Observation ca60d53f-24b2-424c-aab3-2dfccf97843a · outbound

This paper cites Eine Neue Theorie Der Algebraischen Zahlen.

A primer on the closure of algebraic complexity classes under factoring Eine Neue Theorie Der Algebraischen Zahlen

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T23:14:13.040241Z

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Observation 4e3016a2-4be6-426a-9e30-b40b6644d143 · outbound

This paper cites Towards Deterministic Algorithms for Constant-Depth Factors of Constant-Depth Circuits.

A primer on the closure of algebraic complexity classes under factoring Towards Deterministic Algorithms for Constant-Depth Factors of Constant-Depth Circuits

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-06T23:14:14.193159Z

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Unavailable: canonical work link unavailable.

Observation 6cb6e80a-5086-44e3-a80f-807efedee34f · outbound

This paper cites Factoring Polynomials with Rational Coefficients.

A primer on the closure of algebraic complexity classes under factoring Factoring Polynomials with Rational Coefficients

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:14:21.846599Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e7b5c467-322c-4dcf-bde1-ab9ac24cdd6e · outbound

This paper cites Factorization of Polynomials.

A primer on the closure of algebraic complexity classes under factoring Factorization of Polynomials

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-06T23:14:13.238899Z

Source-reported events for the cited work

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Observation c7660367-3e3a-4b3d-8d1f-77bed89cc3ac · outbound

This paper cites Polynˆomes et coefficients.

A primer on the closure of algebraic complexity classes under factoring Polynˆomes et coefficients

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:14:21.401346Z

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Observation 158241db-9b8c-46fa-afbe-7c27234227c6 · outbound

This paper cites an unresolved cited work.

A primer on the closure of algebraic complexity classes under factoring Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-06T23:14:21.074766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2936e5c5-1045-40ad-be14-1e9e963a796b · outbound

This paper cites Deterministically Factoring Sparse Polynomials into Multilinear Factors and Sums of Univariate Polynomials.

A primer on the closure of algebraic complexity classes under factoring Deterministically Factoring Sparse Polynomials into Multilinear Factors and Sums of Univariate Polynomials

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:14:18.047408Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c3dd9e6c-ddc1-43c8-8d9d-faccf682fd66 · outbound

This paper cites On Some Computations on Sparse Polynomials.

A primer on the closure of algebraic complexity classes under factoring On Some Computations on Sparse Polynomials

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:14:17.691215Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c63c35a9-f579-4934-a718-34a92c237448 · outbound

This paper cites Power series in complexity: Algebraic Dependence, Factor Conjecture and Hitting Set for Closure of VP.

A primer on the closure of algebraic complexity classes under factoring Power series in complexity: Algebraic Dependence, Factor Conjecture and Hitting Set for Closure of VP

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:14:19.731965Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 59a51366-1c08-4970-a7d9-99aa6f06aa07 · outbound

This paper cites Deter- ministic Algorithms for Low Degree Factors of Constant Depth Circuits.

A primer on the closure of algebraic complexity classes under factoring Deter- ministic Algorithms for Low Degree Factors of Constant Depth Circuits

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:14:22.364878Z

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Observation e18d5497-3e76-4a8d-b4e2-6b2b17d1c625 · outbound

This paper cites Newton’s Iteration and the Sparse Hensel Algorithm (Extended Abstract).

A primer on the closure of algebraic complexity classes under factoring Newton’s Iteration and the Sparse Hensel Algorithm (Extended Abstract)

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:14:17.148213Z

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Observation ec6a5b13-75da-419e-9d34-dcbd807d7fe0 · outbound

This paper cites Fast Probabilistic Algorithms for Verification of Poly- nomial Identities.

A primer on the closure of algebraic complexity classes under factoring Fast Probabilistic Algorithms for Verification of Poly- nomial Identities

Reference 77

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:14:20.129309Z

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Observation 9801cbb2-e8a7-4b66-8978-9bec7060c8b6 · outbound

This paper cites Discovering the Roots: Uniform Closure Results for Algebraic Classes under Factoring.

A primer on the closure of algebraic complexity classes under factoring Discovering the Roots: Uniform Closure Results for Algebraic Classes under Factoring

Reference 80

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Observation 61e313dd-2ed5-4d2e-943f-60c729c76912 · outbound

This paper cites Hensel Meets Newton–Algebraic Constructions in an Analytic Setting.

A primer on the closure of algebraic complexity classes under factoring Hensel Meets Newton–Algebraic Constructions in an Analytic Setting

Reference 81

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:14:17.397001Z

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Observation 76ae5d6b-3393-4661-a364-e5ab938bd418 · outbound

This paper cites Leibniz Int.

A primer on the closure of algebraic complexity classes under factoring Leibniz Int

Reference 169

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Observation 13ad8cef-58ab-409a-bcf9-fe23197278a8 · outbound

This paper cites Cambridge University Press, Cambridge, 2019 (cit.

A primer on the closure of algebraic complexity classes under factoring Cambridge University Press, Cambridge, 2019 (cit

Reference 170

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Observation 15c83518-a5a5-44db-8a02-63490fadce99 · outbound

This paper cites Dagstuhl, Germany: Schloss Dagstuhl – Leibniz-Zentrum f¨ ur Informatik, 2022, 118:1–118:33 (cit.

A primer on the closure of algebraic complexity classes under factoring Dagstuhl, Germany: Schloss Dagstuhl – Leibniz-Zentrum f¨ ur Informatik, 2022, 118:1–118:33 (cit

Reference 215

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Observation 62cbaaf6-a701-4036-92d5-566fe49e563a · outbound

This paper cites Improved Low-Degree Testing and Its Applications.

A primer on the closure of algebraic complexity classes under factoring Improved Low-Degree Testing and Its Applications

Reference 222

Resolution: unresolved; no resolver link, observed 2026-08-06T23:14:11.076549Z

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Observation d8720c13-cf2a-4c72-b295-30d936be77db · outbound

This paper cites Learning the Coef- ficients: A Presentable Version of Border Complexity and Applications to Circuit Factoring.

A primer on the closure of algebraic complexity classes under factoring Learning the Coef- ficients: A Presentable Version of Border Complexity and Applications to Circuit Factoring

Reference 315

Resolution: unresolved; no resolver link, observed 2026-08-06T23:14:11.404936Z

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Observation e2b06267-1a37-4e49-a6b3-808d8c2184fe · outbound

This paper cites A Probabilistic Remark on Algebraic Program Testing.

A primer on the closure of algebraic complexity classes under factoring A Probabilistic Remark on Algebraic Program Testing

Reference 317

Resolution: unresolved; no resolver link, observed 2026-08-06T23:14:12.474835Z

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Observation 5c1ec71d-085c-4c04-a5ef-79210225e2c8 · outbound

This paper cites Effective Noether Irreducibility Forms and Applica- tions.

A primer on the closure of algebraic complexity classes under factoring Effective Noether Irreducibility Forms and Applica- tions

Reference 583

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Observation f80317b7-7543-40ed-b114-f8800ac8eabc · outbound

This paper cites Efficient Factorization of Polynomials over Local Fields.

A primer on the closure of algebraic complexity classes under factoring Efficient Factorization of Polynomials over Local Fields

Reference 1838

Resolution: unresolved; no resolver link, observed 2026-08-06T23:14:12.134751Z

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Observation 0bbcc061-74e0-41e8-973e-9c5a3f68e3c0 · outbound

This paper cites Derandomization via Symmetric Poly- topes: Poly-time Factorization of Certain Sparse Polynomials.

A primer on the closure of algebraic complexity classes under factoring Derandomization via Symmetric Poly- topes: Poly-time Factorization of Certain Sparse Polynomials

Reference 1858

Resolution: unresolved; no resolver link, observed 2026-08-06T23:14:11.664884Z

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Observation 25ad3ed9-a603-4729-89bc-fdadaec6dc38 · outbound

This paper cites Closure Results for Polynomial Factorization.

A primer on the closure of algebraic complexity classes under factoring Closure Results for Polynomial Factorization

Reference 1903

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Observation 7c6f8fac-b05d-4d50-866a-61ee2010a470 · outbound

This paper cites Factoring High-Degree Polyno- mials by the Black Box Berlekamp Algorithm.

A primer on the closure of algebraic complexity classes under factoring Factoring High-Degree Polyno- mials by the Black Box Berlekamp Algorithm

Reference 2008

Resolution: unresolved; no resolver link, observed 2026-08-06T23:14:13.555238Z

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Observation c2750120-4526-43f8-a6d6-98e98f9b52e0 · outbound

This paper cites 87–100 (cit.

A primer on the closure of algebraic complexity classes under factoring 87–100 (cit

Reference 2011

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Observation 29978904-2ad3-4de7-9a61-2f3dc744de45 · outbound

This paper cites Complexity Theory Column 88: Challenges in Polynomial Factorization.

A primer on the closure of algebraic complexity classes under factoring Complexity Theory Column 88: Challenges in Polynomial Factorization

Reference 2013

Resolution: unresolved; no resolver link, observed 2026-08-06T23:14:12.956483Z

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Observation aaefbdc1-c7b5-4596-bbb5-c857ab27ca52 · outbound

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A primer on the closure of algebraic complexity classes under factoring Unresolved cited work

Reference 2014

Resolution: unresolved; no resolver link, observed 2026-08-06T23:14:13.734689Z

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Observation 057c2fe9-9ff2-4f09-aa82-78e1ffebd6e1 · outbound

This paper cites an unresolved cited work.

A primer on the closure of algebraic complexity classes under factoring Unresolved cited work

Reference 2023

Resolution: unresolved; raw_fallback, observed 2026-08-06T23:14:20.555042Z

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Observation f3a91f7e-ff14-4ecd-bf81-529ed0a33630 · outbound

This paper cites 2367–2386 (cit.

A primer on the closure of algebraic complexity classes under factoring 2367–2386 (cit

Reference 2024

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Observation ac37d540-c9f9-4b3a-85be-57664a83036b · outbound

This paper cites A Case of Depth-3 Identity Testing, Sparse Factorization and Duality.

A primer on the closure of algebraic complexity classes under factoring A Case of Depth-3 Identity Testing, Sparse Factorization and Duality

Reference 2025

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:14:18.815612Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6b2be21a-9953-4176-b09f-48706b0a1270 · outbound

This paper cites Introduction to Geometric Complexity Theory.

A primer on the closure of algebraic complexity classes under factoring Introduction to Geometric Complexity Theory

Reference 2504

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Observation afe11d9c-92f7-4e1c-88ae-c9fd5fe378fb · outbound

This paper cites Determinant versus Permanent.

A primer on the closure of algebraic complexity classes under factoring Determinant versus Permanent

Reference 3821

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Observation 85e2c066-aaff-4fc5-9b7c-ae70acd6a732 · outbound

This paper cites Arithmetic Circuits: A Survey of Recent Results and Open Questions.

A primer on the closure of algebraic complexity classes under factoring Arithmetic Circuits: A Survey of Recent Results and Open Questions

Reference 6198

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:14:18.424814Z

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Pith citing papers

Observation 645f67dd-97e5-4804-8dc4-b069a97bce2a · inbound

Deterministic Algorithms for Low Individual Degree Factors of Sparse Polynomials cites this paper.

Deterministic Algorithms for Low Individual Degree Factors of Sparse Polynomials A primer on the closure of algebraic complexity classes under factoring

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-07-04T15:19:56.575544Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.